The Collaborative International Dictionary of English v.0.48:

Papaw \Pa*paw"\, n. [Prob. from the native name in the West
   Indies; cf. Sp. papayo papaw, papaya the fruit of the papaw.]
   [Written also pawpaw.]
   1. (Bot.) Same as papaya, senses 1 and 2.
      [1913 Webster +PJC]

   2. (Bot.) A tree of the genus Asimina (Asimina triloba),
      growing in the western and southern parts of the United
      States, and producing a sweet edible fruit; also, the
      fruit itself. --Gray.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

papaya \pa*pa"ya\, n. [Prob. from the native name in the West
   Indies; cf. Sp. papayo papaw, papaya the fruit of the papaw.]
   1. (Bot.) A tree (Carica Papaya) of tropical America,
      belonging to the order Passiflore[ae]; called also
      papaw and pawpaw. It has a soft, spongy stem, eighteen
      or twenty feet high, crowned with a tuft of large,
      long-stalked, palmately lobed leaves. The milky juice of
      the plant is said to have the property of making meat
      tender.
      [1913 Webster +PJC]

   2. The fruit of the papaya tree; it is a dull orange-colored,
      melon-shaped fruit, which is eaten both raw and cooked or
      pickled. The fruit contains papain, a protease.
      [1913 Webster + PJC]

WordNet (r) 3.0 (2006):

papaw
    n 1: small tree native to the eastern United States having
         oblong leaves and fleshy fruit [syn: pawpaw, papaw,
         papaw tree, Asimina triloba]
    2: fruit with yellow flesh; related to custard apples [syn:
       papaw, pawpaw]